Maintaining situational awareness of what is happening within a network is challenging, not least because the behaviour happens within computers and communications networks, but also because data traffic speeds and volumes are beyond human ability to process. Visualisation is widely used to present information about the dynamics of network traffic dynamics. Although it provides operators with an overall view and specific information about particular traffic or attacks on the network, it often fails to represent the events in an understandable way. Visualisations require visual attention and so are not well suited to continuous monitoring scenarios in which network administrators must carry out other tasks. Situational awareness is critical and essential for decision-making in the domain of computer network monitoring where it is vital to be able to identify and recognize network environment behaviours. Here we present SoNSTAR (Sonification of Networks for SiTuational AwaReness), a real-time sonification system to be used in the monitoring of computer networks to support the situational awareness of network administrators. SoNSTAR provides an auditory representation of all the TCP/IP protocol traffic within a network based on the different traffic flows between network hosts. SoNSTAR raises situational awareness levels for computer network defence by allowing operators to achieve better understanding and performance while imposing less workload compared to visual techniques. SoNSTAR identifies the features of network traffic flows by inspecting the status flags of TCP/IP packet headers and mapping traffic events to recorded sounds to generate a soundscape representing the real-time status of the network traffic environment. Listening to the soundscape allows the administrator to recognise anomalous behaviour quickly and without having to continuously watch a computer screen.